Try the following questions on discrete probability and independence. The correct anwers are revealed when you submit your answers.

1. Suppose you toss a coin twice in a row showing either heads (\( H \)) or tails (\( T \)) on each toss, for example the outcome could be a tail followed by a head \( (T,H) \). What is the sample space?
2. On a roll of a die what is the probability of getting less than \( 4 \)?
3. The probability it rains on Sunday given that it rained on Saturday is \( \frac{2}{3} \).
The probability it rains on Saturday is \( \frac{1}{3} \). What is the probability it rains on Saturday and doesn't rain on Sunday?